Pythagoras and the Music of the Future is a series of articles in which I discuss, in accessible terms, I hope, the central influence that the harmonic series has had on the development of western music since the Middle Ages. I look closely at the connection between the harmonic series and the conventions of the musical structures of timbre, melody and harmony and musical time i.e. rhythm meter and tempo.
Ironically, or so it might seem, I also argue that whereas the development of functional harmony, and therefore tonality, was strongly influenced by our (probably subliminal) awareness of the interplay of frequency ratios of the harmonic series, the ‘modern’ music that, quite fittingly, has nothing to do with functional harmony, tonality or indeed the notion of regular pulse and tempo is, or should be, equally bound up with the very same underlying proportions.
The planned fourth article will make the case for a musical ‘language’ that utilises the gamut of proportions inherent in the naturally occurring overtone series first postulated by Pythagoras. I will further argue that the realisation, and indeed the performance, of such a music, is made possible only via the availability of manageable and affordable digital computers together with allied software for sound generation and organisation.
Although the earliest article was published over two years ago, the series as a whole maintains a steady flow of views, which seems to have gathered momentum recently. Why not take a look yourself;
Klee Connections for Piano was composed in February 2013. It works by connections being formed between superimposed variants of very simple rhythmic and harmonic series. Some of these connections are made by the composer – using them as a means of developing basic material – and by the listener who may well perceive patterns that weren’t deliberately put there, but which arise out of the interactions of these elements. For example, the sequences, inversions and cadence-like configurations that are often suggested are, to a greater or lesser extent, coincidental or even ‘accidental’.
This is something that the painter Paul Klee made use of in his work: interactions between lines or shapes often give rise to configurations that are not independently drawn and/or which have an aspect of familiarity.
Although this work is written in a post-tonal idiom the word series is used here not in the sense of ‘twelve-tone’ or serial music. An alternative might have been sequence, but of course, that too has a musical definition that would, in this context, be even more misleading.
Click below to listen while following the score on YouTube.
It shouldn’t be too long before I can post my next article in the series ‘Pythagoras and the Music of the Future’. It has taken me some time partly because I have made a start on ‘digitising’ some of my earlier compositions to enable sharing.
The first fruits of this will appear in my next post introducing my composition, Songs of The Aristos for brass & computer-generated tape. The accompanying sound file was created using Sibelius 7 and the marvellous, free sound recording software Audacity. I am still ‘finding my way’, especially with the latter, so any audio clips that I post may leave something to be desired in terms of ‘engineering’. Please forgive.
Going back to Pythagoras and the harmonic series for a moment, I want to share a quote I recently came across, which I have a great deal of sympathy with. It’s from A Monk’s Musical Musings – an excellent, very comprehensive blog by a scholarly guitarist who goes by the nom de plume ‘Hucbald‘.
“Lacking in all music theories that I am aware of from Western history is a neat and tidy description of why music works, and why it has evolved as we see from the historical record. There is no Einsteinian General Theory of Musical Relativity… yet.
For such a proposed theory to be compelling, it would have to relate directly – in all of its aspects – to the very nature of sound itself. Harmony, counterpoint, rhythm, melody, and form would all have to be explained as having originated within some feature that God and nature have given to sound, and sound alone. There is only one candidate for the feature I am describing, of course, and that is The Harmonic Overtone Series.”
I couldn’t agree more with the second paragraph. In fact, I think that study of the harmonic series could probably lead to a musical ‘Theory of Everything’ let alone Relativity! The problem for me is that Hucbald doesn’t seem to have much time for ‘modern’ i.e. non-tonal music judging by subsequent comments in his blog. It’s almost as if he holds the belief (and if he doesn’t many others do) that post tonal music has somehow become divorced from the properties of the harmonic series. I can only agree to a certain extent and this is something I’ll be addressing in my forthcoming articles.
Nevertheless, for those interested in such things, there is a lot to be gained from looking at;
I am just about ready to introduce the first in a projected series of articles discussing, in accessible terms I hope, the influence that the harmonic series has had on musical development since the Middle Ages. I will be discussing not only the connection between the harmonic series and timbre (the obvious one), but also the connections between this and the conventions governing musical structures such as rhythm, melody and harmony.
Ultimately, I will arrive at the conclusion that there needs to be a clear, natural (as opposed to contrived), relationship between the the diverse sets of proportions inherent in the harmonic series, and musical expression – now and in the future. Ironically, or so it might seem, I will also argue that whereas the development of functional harmony and therefore tonality was strongly influenced by our perception (maybe subliminal – I don’t know) of the ‘inner workings’ of musical sound, the music that has already left, and will leave, tonality where it belongs – in the past – is equally bound up with these inner workings – particularly as represented by the harmonic series.
Many will know a great deal about the relationship between the harmonic series and timbre already, so may not find anything particularly new in the first article which sets the scene, so to speak. To find out if you’re one of them, click here.